The La Liga side's 34th-minute opener came when Steve Gohouri's sliding clearance rebounded off Marco Perez who raced into the penalty area only to be brought down by goalkeeper Chris Kirkland.
Jorge Lopez converted from the spot but an even worse error led to the equaliser seconds before half-time when Carlos Diogo rolled a free-kick straight into the path of Ben Watson.
After moving the ball on, the midfielder eventually laid on the pass for Charles N'Zogbia to round goalkeeper Leo Franco.
However, 15 minutes from time Braulio Nobrega capitalised on a quick ball forward to clip past Kirkland before Gabriel Fernandez smashed in an unstoppable 35-yard effort.
A number of Roberto Martinez's new signings featured, with club-record transfer Mauro Boselli, the former Estudiantes striker, showing some good touches but looking short of match sharpness.